Computer Science
Reduce the following boolean function with the help of Karnaugh's map:
F (a, b, c, d) = Σ (1, 2, 3, 11, 12, 14, 15)
Answer
From Pair (1,3):
Rows representing the pair: a'b'
Columns representing the pair: c'd + cd = d
Term Obtained = a'b'd
From Pair (3,2):
Rows representing the pair: a'b'
Columns representing the pair: cd + cd' = c
Term Obtained = a'b'c
From Pair (12,14):
Rows representing the pair: ab
Columns representing the pair: c'd' + cd' = d'
Term Obtained = abd'
From Pair (15,11):
Rows representing the pair: ab + ab' = a
Columns representing the pair: cd
Term Obtained = acd
Pairs (15,14) and (3,11) are redundant
Simplified expression = a'b'd + a'b'c + abd' + acd
Related Questions
Reduce the following boolean function with the help of Karnaugh's map:
F (A, B, C, D) =Σ (0, 1, 2, 3, 12, 13, 14, 15)
Find the complement of the following expressions:
(a) (A + B).(B + C).(A + C)
(b) A.B + (A'.B').(B.C + B'.C')
Reduce the following boolean function with the help of Karnaugh's map:
F (a, b, c, d) =Σ (0, 1, 2, 4, 5, 6, 8, 9, 12, 13, 14)
What do you understand by Karnaugh's map? Explain.